A Natural History of Entropy, or, How to Refute Eternal Recurrence

by Yule Heibel on August 15, 2003

I’ve been reading Jorge Luis Borges lately, and was blown away by his 1934 essay, “The Doctrine of Cycles.” Since this is my blog and I can post anything I want, I’m going to write about it. Too bad if anyone thinks it’s too esoteric or too long. First, I don’t know whether I should feel encouraged or defeated by Borges’s laconic refutation of Friedrich Nietzsche’s doctrine of Eternal Recurrence. For one thing, it’s achieved at the price of the universe’s eventual death. But for another, I’m with Borges on this, even though it is an almost scary and nearly friendless argument that he makes to demolish Nietzsche. First, Borges considers infinity, and calls on mathematics in the person of Georg Cantor to explain why Nietzsche is wrong. Cantor’s “heroic theory of sets” (Borges) proves that in an infinity of atoms, nothing need ever “return”:

The series of natural numbers is very orderly, that is, the terms that form it are consecutive: 28 precedes 29 and follows 27. The series of points in space (or of instants in time) cannot be ordered in the same way: no number has a successor or an immediate predecessor. It is like a series of fractions arranged in order of magnitude. What number will we count after 1/2? Not 51/100, because 101/200 is closer; not 101/200, because 201/400 is closer; not 201/400, because … According to Cantor, the same thing happens with points. We can always interpose more of them, in infinite numbers. Therefore we must try not to conceive of decreasing sizes. Each point is ‘already’ the final degree of an infinite subdivision.
The clash between Cantor’s lovely game and Zarathrustra’s lovely game is fatal to Zarathrustra. If the universe consists of an infinite number of terms, it is rigourously capable of an infinite number of combinations — and the need for a Recurrence is done away with. There remains its mere possibility, which can be calculated as zero. (p.117)

But it’s Borges’s closing argument, calling on the theory of entropy to demolish “eternal recurrence,” which is most convincing, and simultaneously awesome:

Heat and light are no more than forms of energy. It suffices to project a light onto a black surface to convert it into heat. Heat, however, will never return to the form of light. This inoffensive or insipid-seeming proof annuls the ‘circular labyrinth’ of the Eternal Return.
The first law of thermodynamics declares that the energy of the universe is constant; the second, that this energy tends toward isolation and disorder, though its total quantity does not decrease. This gradual disintegration of the forces that make up the universe is entropy. Once maximum entropy is reached, once different temperatures have been equalized, once any action of one body on another has been neutralized (or compensated for), the world will be a random assemblage of atoms. In the deep center of the stars, this difficult, mortal equilibrium has been achieved. By dint of constant interchange, the whole universe will reach it, and will be warm and dead.

Light is gradually lost in the form of heat; the universe, minute by minute, is becoming invisible. It grows more inconstant, as well. At some point, it will no longer be anything but heat: an equilibrium of immobile, evenly distributed heat. Then it will have died. (p.122)

With that, Borges shows that entropy refutes Nietzsche’s doctrine of Eternal Recurrence.
Somewhere inbetween these two arguments, he seems to suggest that mono- and atheism are the only two respectable positions that an intellectual can take in regard to religion. Philosophers and theologians before Nietzsche postulated theories of Eternal Recurrence, and St. Augustine, Borges points out, refuted “so abominable a doctrine” for “the gaudy futility of this wheel” and for “the ridiculousness of the Logos dying on the cross like an acrobat in an interminable sequence of performances.” (p.118) St. Augustine derides the Stoics and Pythagoreans who theorize Eternal Recurrence as “worthless revolutions and affirms that Jesus is the straight path that allows us to flee from the circular labyrinth of such deceptions.” (ibid.)
But where does Borges come to rest? He doesn’t. Here’s his closing paragraph:

A final uncertainty, this one of a metaphysical order. If Zarathrustra’s hypothesis is accepted, I do not fully understand how two identical processes keep from agglomerating into one. Is mere succession, verified by no one, enough? Without a special archangel to keep track, what does it mean that we are going through the thirteen thousand five hundred and fourteenth cycle and not the first in the series or number three hundred twenty-two to the two thousandth power? Nothing, in practice — which is no impairment to the thinker. Nothing, for the intellect — which is serious indeed.

If we stop differentiating, then as intellectuals we’re dead. Eternally.


jr August 17, 2003 at 9:59 pm

So can the universe be expanding and contracting without recurrence? The even distribution idea bothers me. Since there wasn’t (I have no proof) an even distribution of light in the beginning which was necessary for us to be here to think about recurrence is there a posiblity that there won’t be an even distribution of heat in the end.

Yule Heibel August 18, 2003 at 2:43 am

Of course I don’t know how to answer that. The universe could be a one-way ride, or it could be a breath. But the notion of a Return to anything even remotely resembling a This seems mighty unlikely.

Joel August 18, 2003 at 4:29 am

How does Borges explain waves on the beach? Does “recurrence” need to be perfect every time or just enough like other events to be recognizable as “like them”?

There are physicists out there who speculate now that the Universe stops expanding, it will fold back on itself, repeating where it has been.

I don’t know that we can prove or disprove recurrence on this scale. It wouldn’t follow that we — in a new reincarnation in a new breath of the Universe — would even be aware that we’d existed the last time that the Universe expanded and contracted.

I file this away under unprovables, a question about causes and ends that we won’t be around to see. A bit like the Book of Revelations and Genesis. I must ask “Are they necessary to think about anything?” I don’t believe so.

Yule Heibel August 19, 2003 at 1:32 am

I like to think about this, even if it’s not strictly speaking “necessary.” I think it does have repercussions in our everyday lives inasmuch as we may or may not get sucked into variants of mysticism, or inasmuch as having a sceptical mindset vis-a-vis something like eternal recurrence, we temper our own quotidien “adjustments” (believing in what goes ’round comes ’round, or whatever else you/I/we tell ourselves in daily doings). And finally, Borges suggests that eternal recurrence results in a mental agglomeration (a mush of stuff), which for an intellectual would be intolerable.

Zero Omega December 7, 2006 at 2:14 am

I think you are missing the point about Nietzsche’s “doctrine” of eternal return. Eternal return is the “central idea” in Nietzsche’s philosophy because it HAS NO CONTENT for US – we can be only “buffoons and barrel organs” by repeating it – jackasses meaninglessly repeating words by rote that can mean nothing to us – or cows merely “ruminating” (or regurgitating).
The final point of Thus Spoke Zarathustra is thus to break us of the habit of listening to sermons.
He’s not trying to tell the truth!

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